Dynamic Knapsack Model Report

Parameters

Model Parameters

This model is a smaller instance of the full problem:

  • Planning horizon is decreased from 24 weeks to 10 weeks
  • Maximum tracked wait is decreased from 6 weeks to 4 weeks
  • There are 3 surgeries instead of 6 surgeries
  • Number of priorities is set to 1

Simulation Parameters

  • 30 Replications
  • 1250 weeks duration
  • 250 weeks warm up

Surgeries

  1. Surgery 1 - 1. SPINE POSTERIOR DECOMPRESSION/LAMINECTOMY LUMBAR
  2. Surgery 4 - 4. SPINE POST CERV DECOMPRESSION AND FUSION W INSTR
  3. Surgery 6 - 6. SPINE POSTERIOR DISCECTOMY LUMBAR

Arrival Rate

It was set to be 95% of the capacity, however due to transitions, the resource usage should be higher than 95%

Surgery Complexity Arrival_Adjusted Arrival_Original Rationale
Surgery 1 Complexity 1 1.2319885 1.0000 once per week
Surgery 1 Complexity 2 0.6159942 0.5000 once per two weeks
Surgery 4 Complexity 1 0.1437320 0.0833 once per 3 months
Surgery 4 Complexity 2 0.1026657 0.0625 once per 4 months
Surgery 6 Complexity 1 1.2319885 1.0000 once per week
Surgery 6 Complexity 2 0.6159942 0.5000 once per 2 weeks

Resource Usage

Usage of the resources

Surgery Complexity Resource_Type Usage
Surgery 1 Complexity 1 Admissions 0.0
Surgery 1 Complexity 1 OR_Time 3.0
Surgery 1 Complexity 2 Admissions 1.0
Surgery 1 Complexity 2 OR_Time 4.0
Surgery 4 Complexity 1 Admissions 1.0
Surgery 4 Complexity 1 OR_Time 4.0
Surgery 4 Complexity 2 Admissions 1.0
Surgery 4 Complexity 2 OR_Time 5.5
Surgery 6 Complexity 1 Admissions 0.0
Surgery 6 Complexity 1 OR_Time 1.5
Surgery 6 Complexity 2 Admissions 0.0
Surgery 6 Complexity 2 OR_Time 2.5

Resource Capacity

Resouce Capacity_Weekly Unit
Admissions 1.50 Patients Admitted per week
OR_Time 11.25 OR Hours per week

R1R2 Report

This model is the default model that does not penalize bed under utilization

Policy Description

The description will be based on the following graphs (both of them are for M of 0 only):

The top graphs show MDP policy, and the graphs below show Myopic policy.

The graph on the left shows in which days the policy will allow scheduling. If the value is below 0 - the model will allow scheduling, otherwise the model will keep patients in the waitlist. Thus this policy will only schedule into week 1 and week 2. The plot on the right shows the approximate priority of different surgeries. The lower the surgery is on the list the more likely it is to be scheduled first. The following is the order:

  • Surgery 6, Complexity 2
  • Surgery 6, Complexity 1
  • Surgery 1, Complexity 1
  • Surgery 1, Complexity 2
  • Surgery 4, Complexity 1
  • Surgery 4, Complexity 2

For Myopic, it is changed such that the entire horizon is filled. And the graph on the right shows the approximate order of scheduling priority. It appears to be very similar to MDP.

Additionally the following graphs give some insights on how the policy makes decision

Policy Results

Wait Times in weeks

policy Overall Surgery1 Surgery4 Surgery6
MDP 7.28 += 9.16 14.11 += 12.85 5.98 += 2.83 0.56 += 0.22
myopic 14.76 += 14.08 27.15 += 19.43 17.35 += 4.28 1.91 += 0.71

Wait List Size

policy Overall Surgery1 Surgery4 Surgery6
MDP 29.25 += 7.38 26.73 += 7.21 1.49 += 0.57 1.03 += 0.43
myopic 58.52 += 12.2 50.74 += 11.84 4.28 += 0.94 3.51 += 0.73

Utilization

policy bed OR
MDP 57.1 += 14.05 94.89 += 7.13
myopic 63.05 += 12.36 95.39 += 6.85

Reschedules as percentage of arrivals & Total Reschedules

policy Overall Surgery1 Surgery4 Surgery6
MDP 2.6 += 0.11 3.6 += 0.17 5.4 += 0.59 1.22 += 0.08
myopic 12.74 += 0.33 14.9 += 0.41 71.39 += 4.52 2.78 += 0.17

Transitions per week

policy Overall Surgery1 Surgery4 Surgery6
MDP 1.14 += 0.09 0.93 += 0.09 10.78 += 0.87 0.08 += 0.02
myopic 8.61 += 0.33 10.46 += 0.37 40.83 += 2.19 2.46 += 0.15

R1R2R3 Report

In addition to the parameters above, this model penalizes bed under utilization in the first period

Policy Description

Additionally the following graphs give some insights on how the policy makes decision

Policy Results

Wait Times in weeks

policy Overall Surgery1 Surgery4 Surgery6
MDP 8.93 += 4.26 14.2 += 4.6 8.99 += 6.9 3.61 += 2.01
myopic 26.21 += 21.96 19.35 += 6.34 109.81 += 71.79 22.01 += 13.38

Wait List Size

policy Overall Surgery1 Surgery4 Surgery6
MDP 35.45 += 4.62 26.46 += 3.58 2.24 += 1.04 6.75 += 2.07
myopic 103.97 += 22.92 36.02 += 7.34 27.3 += 10.22 40.66 += 9.13

Utilization

policy bed OR
MDP 116.56 += 12.66 103.03 += 10.79
myopic 120.18 += 12.61 100.18 += 6.88

Reschedules as percentage of arrivals & Total Reschedules

policy Overall Surgery1 Surgery4 Surgery6
MDP 65.78 += 0.65 59.42 += 1.63 0 += NA 80.88 += 2.46
myopic 80.44 += 3.39 37.64 += 6.73 0 += NA 134.34 += 12.61

Transitions per week

policy Overall Surgery1 Surgery4 Surgery6
MDP 24.67 += 0.3 48.87 += 0.61 0.2 += 0.1 3.52 += 0.19
myopic 31.41 += 2.06 55.86 += 3.78 7.61 += 1.12 9.91 += 0.52